Question

Prove that the sum of all angles of a quadrilateral is 360 degree

Answer 1

Prove that the sum of all the four angles of a quadrilateral is 360°. 

Proof: Let ABCD be a quadrilateral. Join AC. 

Clearly, ∠1 + ∠2 = ∠A ...... (i) 

And, ∠3 + ∠4 = ∠C ...... (ii) 

We know that the sum of the angles of a triangle is 180°. 
Therefore, from ∆ABC, we have

∠2 + ∠4 + ∠B = 180° (Angle sum property of triangle)

From ∆ACD, we have 

∠1 + ∠3 + ∠D = 180° (Angle sum property of triangle) 

Adding the angles on either side, we get; 

∠2 + ∠4 + ∠B + ∠1 + ∠3 + ∠D = 360° 

⇒ (∠1 + ∠2) + ∠B + (∠3 + ∠4) + ∠D = 360° 

⇒ ∠A + ∠B + ∠C + ∠D = 360° [using (i) and (ii)]. 

Hence, the sum of all the four angles of a quadrilateral is 360°.

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Answer 2

let us consider a quadrilateral ABCD ,

in a quadrilateral we have ,

           angle A = 90 degree ( perpendicular )

           similarly all angles B,C,D. ARE 90 degree .

hence, we total all angles we get 90+90+90+90 which is equal to 360 degree